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A
review of statistics
Clement Radcliffe, Contributor
I have chosen to review statistics
with you this week. Statistics, at
this level, may be summarised as:
- Collection
of data
- Presentation
of data
- Analysis
of data
Collection
of data
The
usual methods are:
(a)
Experiment - measuring or counting
(b)
Research
(c)
Interviews
Methods
of presentation
The
methods which are usually used are:
Bar
chart
- Data
is represented by rectangular bars
of equal width
- The
bars are separated
- The
area of each bar is proportional
to the quantity represented
Example:
Represent
the following modes of transportation
on a bar graph.
Mode
of transportation
Bus
Private
Other
Number
of persons
840
320
1560
Pie
chart
The
circle is divided into sectors, the
size of each sector being proportional
to the quantities represented.
Example
Represent
the modes of transportation given
above on a pie chart.
PIE
CHART
Histogram
Points
to note
- This
is used when the data is presented
in terms of frequency.
- The
information is represented by vertical
bars; all are of equal width and
are joined side by side.
- Both
axes must be carefully labelled
and the appropriate scales used.
If a scale is given, it MUST be
used EXACTLY.
- The
frequency is always represented
on the vertical axis.
- The
frequency of each observation or
variable is proportional to the
height of the bar.
- Be
sure that you are familiar with
the principle of boundary values.
You
are urged, when constructing the histogram,
to avoid the following common errors:
a)
Separating the bars
b)
Incorrectly labelling the horizontal
axis (scores)
c)
Confusing the histogram with other
methods of presentation, for example,
bar graph or frequency polygon.
The
following is an example of the use
of the histogram to represent the
results of a math test.
Example
The
following scores were obtained by
40 students who sat a math test. Use
a histogram to represent the results.
5,
4, 0, 1, 6, 5, 7, 5, 9, 2, 1, 8, 4,
4, 3, 2, 7, 8, 5, 5, 4, 7, 4, 6, 3,
1, 3, 4, 5, 7, 6, 5, 8, 3, 5, 7, 3,
9, 4, 6
The
above data should be summarised in
the frequency table as follows:
| Scores |
0
|
1
|
|
2
|
3
|
4
|
5
|
|
6
|
7
|
8
|
9
|
|
Frequency
|
1
|
3
|
|
2
|
5
|
7
|
8
|
|
4
|
5
|
3
|
2
|
It
is always necessary to construct the
frequency table if it is not given.
Points
to note
- It
is more convenient to form a tally
table in determining the frequency
table.
- The
scores are discrete values and represent
the values of the respective bars.
- The
scores may be in the form of grouped
data and hence each bar represents
a range of values.
- The
method required to construct a histogram
for grouped data is similar to that
for discrete data.
The
information given above is illustrated
in the following homework:
(1)
Express the following scores in a
frequency table and plot the histogram.
22,
15, 0, 22, 11, 9, 0 14, 20, 9, 16,
5, 11, 24, 16, 5, 11, 24, 5, 5, 22,
15, 9, 9, 11
(2)
The table below shows the number of
inches of rainfall which fell over
a period of time.
Inches
of Rainfall
0-4
5-9 10-14 15-19
20-24
25-29
Number
of days
5
8 3 1 2 1
Using
a scale of two cm to represent five
inches on the X axis, and one cm to
represent one day on the Y axis, construct
the histogram to represent the data.
Have
a very good week.
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Darren
Fraser explains a topic to students
during a CXC symposium on mathematics
at Bridgeport High School on
April 12.
- Anthony Minott/Freelance
Photographer
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Clement
Radcliffe is the principal of Glenmuir
High School in May Pen.
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